Stress–Strain Relationship for Metal Hollow Sphere Materials as a Function of Their Relative Density

Abstract

The stress–strain relationship for uniaxial compression of a metal hollow sphere material in large strains is obtained using a simplified model for the spheres’ deformation within a 3D block assuming a hexagonal packing pattern. The yield strength and material strain hardening are obtained as functions of the relative density in two characteristic loading directions. The expression for the stress–strain relationship consisting of quadratic and linear terms with respect to the relative density is linked to the partitioning of the deformation energy during compression. The theoretical predictions are compared with limited test results on mild steel hollow sphere material and finite element simulation results obtained by our group.